Signal processing method, signal processing apparatus, and signal processing program

ABSTRACT

A desired signal is extracted with a higher accuracy from a mixed signal wherein a plurality of signals are mixed. At the time of extracting a first signal from a first mixed signal and a second mixed signal, said first mixed signal and second mixed signal having the first signal and second signal mixed therein, an estimate value of the first signal in the past is obtained as a first estimate value, and an estimate value of the second signal in the past is obtained as a second estimate value. Then, a first isolation signal is generated by subtracting the second estimate value from the first mixed signal, and a second isolation signal is generated by subtracting the first estimate value from the second mixed signal. Then, the signal generated using the first isolation signal and the second isolation signal is outputted as the first signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a National Stage of International Application No. PCT/JP2010/067121 filed Sep. 30, 2012, claiming priority based on Japanese Patent Application No. 2009-229509. filed Oct. 1, 2009, the contents of all of which arc incorporated herein by reference in their entirety.

TECHNICAL FIELD

The present invention relates to a signal processing technique for extracting a desired signal from a mixed signal in which a plurality of signals are mixed.

BACKGROUND ART

There are signal processing techniques for extracting a desired signal from a plurality of mixed signals. For example, a noise canceller (noise eliminating system) is a system for eliminating a noise superimposed over a desired voice signal (referred to hereinbelow as a desired signal). NPL 1 discloses a method of eliminating a noise using an adaptive filter. The method eliminates a noise by using an adaptive filter to estimate properties of an acoustic channel from a noise source to a microphone, processing a signal having a correlation with a noise (referred to hereinbelow as a noise-correlated signal) by the adaptive filter to produce a pseudo noise, and subtracting the pseudo noise from a mixed signal over which a noise is superimposed.

According to the technique disclosed in NPL 1, a desired signal component, sometimes referred to as crosstalk, may leak into the noise-correlated signal, and when a pseudo noise is produced using the noise-correlated signal having a crosstalk, part of an output signal is subtracted to cause distortion in the output signal. As a configuration for preventing such distortion, a cross-coupled noise canceller is disclosed in NPL 2, in which an adaptive filter capable of handling a crosstalk is installed to produce a pseudo crosstalk so that the noise and crosstalk are eliminated at the same time.

The “cross-coupled noise canceller” disclosed in NPL 2 will now be explained with reference to FIG. 10. A desired signal s₁(k) from a desired signal source 910 can be assumed to be convolved with an impulse response h₁₁ (a transfer function H₁₁) of an acoustic space from the desired signal source 910 to a microphone 901 before the signal s₁(k) reaches the microphone 901. On the other hand, a noise s₂(k) from the noise source 920 can also be assumed to be convolved with an impulse response h₂₁ (a transfer function H₂₁) of an acoustic space from the noise source 920 to the microphone 901 before the noise s₂(k) reaches the microphone 901. Therefore, a voice signal x₁(k) output from the microphone 901 at a time k is a mixed signal expressed by EQ. (1) below.

Similarly, the desired signal s₁(k) from the desired signal source 910 can be assumed to be convolved with an impulse response h₁₂ (a transfer function H₁₂) of an acoustic space from the desired signal source 910 to a microphone 902 before the signal s₁(k) reaches the microphone 902. On the other hand, the noise s₂(k) from the noise source 920 can also be assumed to be convolved with an impulse response h₂₂ (a transfer function H₂₂) of an acoustic space from the noise source 920 to the microphone 902 before the noise s₂(k) reaches the microphone 902. Therefore, a voice signal x₂(k) output from the microphone 902 at the time k is a mixed signal expressed by EQ. (2) below.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack & \; \\ {{x_{1}(k)} = {{\sum\limits_{j = 0}^{{M\; 1} - 1}{{h_{11}(j)}{s_{1}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 1} - 1}{{h_{21}(j)}{s_{2}\left( {k - j} \right)}}}}} & (1) \\ \left\lbrack {{Equation}\mspace{14mu} 2} \right\rbrack & \; \\ {{x_{2}(k)} = {{\sum\limits_{j = 0}^{{N\; 2} - 1}{{h_{12}(j)}{s_{1}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{M\; 2} - 1}{{h_{22}(j)}{s_{2}\left( {k - j} \right)}}}}} & (2) \end{matrix}$

In these equations, h₁₁(j), h₁₂(j), h₂₁(j), h₂₂(j) correspond to the transfer functions H₁₁, H₁₂, H₂₁, H₂₂ each representing an impulse response at a sample index j. M1, M2, N1, N2 each represent the length of the impulse response in the mixing process, which is the number of taps in transforming the transfer functions H₁₁, H₁₂, H₂₁, H₂₂ into a filter. M1, M2, N1, N2 are related to the distances from the desired signal source 910 to the microphone 901, from the noise source 920 to the microphone 902, from the noise source 920 to the microphone 901, and from the desired signal source 910 to the microphone 902, and acoustic properties of the space, etc.

Especially, when the microphone 901 lies sufficiently close to the desired signal source 910, M1−1=0 and h₁₁(0)=1, so that EQ. (1) can be rewritten into EQ. (3) below.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 3} \right\rbrack & \; \\ {{x_{1}(k)} = {{s_{1}(k)} + {\sum\limits_{j = 0}^{{N\; 1} - 1}{{h_{21}(j)}{s_{2}\left( {k - j} \right)}}}}} & (3) \end{matrix}$

Similarly, when the microphone 902 lies sufficiently close to the noise source 920, M2−1=0 and h₂₂(0)=1, so that EQ. (2) can be rewritten into EQ. (4) below.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack & \; \\ {{x_{2}(k)} = {{\sum\limits_{j = 0}^{{N\; 2} - 1}{{h_{12}(j)}{s_{1}\left( {k - j} \right)}}} + {s_{2}(k)}}} & (4) \end{matrix}$

At that time, an output y₁(k) of a subtractor 903 is a signal obtained by subtracting an output u₁(k) of an adaptive filter 907 from the signal x₁(k) of the microphone 901, as expressed by EQ. (5) below. On the other hand, y₂(k) is signal obtained by subtracting an output u₂(k) of an adaptive filter 908 from the signal x₂(k) of the microphone 902, as expressed by EQ. (6) below. In these equations, w_(21,j)(k), w_(12,j)(k) are coefficients of the adaptive filters 907, 908.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 5} \right\rbrack & \; \\ {{y_{1}\;(k)} = {{{x_{1}(k)} - {u_{1}(k)}} = {{x_{1}(k)} - {\sum\limits_{j = 0}^{{N\; 1} - 1}{{w_{21,j}(k)}{y_{2}\left( {k - j} \right)}}}}}} & (5) \\ \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack & \; \\ {{y_{2}(k)} = {{{x_{2}(k)} - {u_{2}(k)}} = {{x_{2}(k)} - {\sum\limits_{j = 0}^{{N\; 2} - 1}{{w_{12,j}(k)}{y_{1}\left( {k - j} \right)}}}}}} & (6) \end{matrix}$

That is, the output u₁(k) of the adaptive filter 907 is a pseudo noise, and the output u₂(k) of the adaptive filter 908 is a pseudo crosstalk. Ultimately, y₁(k) is output as a signal whose noise is eliminated at the noise canceller.

From the above EQs. (3) and (5), the noise-free signal output y₁(k) is given by the following equation.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack & \; \\ {{y_{1}(k)} = {{s_{1}(k)} + {\sum\limits_{j = 0}^{{N\; 1} - 1}{{h_{21}(j)}{s_{2}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 1} - 1}{{w_{21,}(k)}{y_{2}\left( {k - j} \right)}}}}} & (7) \end{matrix}$

That is, y₁(k)=s₁(k) stands when y₂(k)=s₂(k) and w_(21,j)(k)=h₂₁(j), (j=0, 1, 2, . . . , N1−1), where perfect noise elimination can be achieved.

On the other hand, a system that can separate two signals in a similar configuration to that shown in FIG. 10 is disclosed in NPL 3 (a feed-back blind signal separation system). The feed-back blind signal separation system disclosed in NPL 3 will now be described with reference to FIG. 11. FIG. 11 is different from FIG. 10 in that the output y₂(k) of the subtractor 904 is output as one of the extracted signals. Moreover, coefficients for adaptive filters 917, 918 are updated using y₁(k) and y₂(k) at a coefficient updating section 981.

In the blind signal separation system shown in FIG. 11, again, EQ. (7) stands when the microphones 901 and 902 lie sufficiently close to a first signal source 910 and a second signal source 930, respectively. Likewise, EQ. (8) below stands for y₂(k).

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack & \; \\ {{y_{2}(k)} = {{s_{2}(k)} + {\sum\limits_{j = 0}^{{N\; 2} - 1}{{h_{12}(j)}{s_{1}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 2} - 1}{{w_{12,j}(k)}{y_{1}\left( {k - j} \right)}}}}} & (8) \end{matrix}$

Since perfect signal separation is achieved only when y₁(k)=s₁(k) and y₂(k)=s₂(k) stand, the following two equations should stand as a requirement therefor. w _(21,j)(k)=h ₂₁(j), j=0, 1, 2, . . . , N1−1 w _(12,j)(k)=h ₁₂(j), j=0, 1, 2, . . . , N2−1

NPL 3 addresses a general case in which a condition that the microphone 901 and microphone 902 should lie sufficiently close to the first signal source 910 and second signal source 930 is not satisfied, and provides a requirement that the following equations should stand for perfectly separating signals. w _(21,j)(k)=h ₂₁(j)/h ₂₂(j), j=0, 1, 2, . . . , N1−1 w _(12,j)(k)=h ₁₂(j)/h ₁₁(j), j=0, 1, 2, . . . , N2−1

CITATION LIST Non Patent Literature

NPL 1: B. Widrow, “Adaptive Noise Cancelling: Principles and Applications,” Proceedings of the IEEE, vol. 63, pp. 1692-1716, December 1975

NPL 2: M. J. Al-Kindi and J. Dunlop, “A low distortion adaptive noise cancellation structure for real time applications,” Proceedings of ICASSP 1987, vol. 12, pp. 2153-2156, April 1987

NPL 3: K. Nakayama, A. Horita and A. Hirano, “Effects of propagation delays and sampling rate on feed-back BSS and comparative studies with feed-forward BSS,” Proceedings of EUSIPCO 2008, 16^(th) European Signal Processing Conference, Lausanne, Switzerland, CD-ROM, September 2008

SUMMARY OF INVENTION Technical Problem

In the configurations disclosed in NPLs 2 to 3 above, however, to extract a desired signal from a mixed signal, current values (values at time k) of “other output signals” output as other signals (signals other than the desired signal) contained in the mixed signal are theoretically required. On the other hand, to determine the current values of the “other output signals,” a current value of the “desired output signal” output as the desired signal is required, thus posing a problem of reciprocity. Accordingly, coefficients (w_(12,0)(k) and w_(21,0)(k) in the example shown in FIG. 11) corresponding to the current values of other output signals are set to zero in the filter to ignore them. Therefore, a desired signal may not successfully be extracted with accuracy, leading to degradation of quality of extracted output signals.

As such, an object of the present invention is to provide a signal processing technique to solve the aforementioned problem.

Solution to Problem

To attain the object described above, a signal processing method according to the present invention for extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, is characterized in comprising: determining an estimated value of said first signal in the past as a first estimated value; determining an estimated value of said second signal in the past as a second estimated value; removing said second estimated value from said first mixed signal to produce a first separated signal; removing said first estimated value from said second mixed signal to produce a second separated signal; and outputting a signal produced using said first separated signal and said second separated signal as said first signal.

To attain the object described above, another signal processing method according to the present invention for extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, is characterized in comprising: for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing the estimated values from an m-th mixed signal to produce an m-th separated signal; and producing a signal using said first to n-th separated signals, and outputting the signal as said first signal.

To attain the object described above, a signal processing apparatus according to the present invention is characterized in comprising: a first filter for producing, from a first mixed signal generated to have a first signal and a second signal mixed, an estimated value of said second signal in the past as a second estimated value; a first subtracting section for removing said second estimated value from said first mixed signal to produce a first separated signal; a second filter for producing, from a second mixed signal generated to have the first signal and second signal mixed, an estimated value of said first signal in the past as a first estimated value; a second subtracting section for removing said first estimated value from said second mixed signal to produce a second separated signal; and an output section for outputting a signal produced using said first separated signal and said second separated signal as said first signal.

To attain the object described above, another signal processing apparatus according to the present invention is characterized in comprising: a filter for, for each natural number m from 1 to n, producing, from first to n-th mixed signals generated to have n signals from a first signal to an n-th signal mixed, estimated values of the first to n-th signals in the past other than an m-th signal in the past; a subtracting section for removing said estimated values from said first to n-th mixed signals to produce first to n-th separated signals; and an output section for outputting a signal produced using said first to n-th separated signals as said first signal.

To attain the object described above, a signal processing program according to the present invention causes a computer to execute: for extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, processing of determining an estimated value of said first signal in the past as a first estimated value; processing of determining an estimated value of said second signal in the past as a second estimated value; processing of removing said second estimated value from said first mixed signal to produce a first separated signal; processing of removing said first estimated value from said second mixed signal to produce a second separated signal; and processing of outputting a signal produced using said first separated signal and said second separated signal as said first signal.

To attain the object described above, another signal processing program according to the present invention causes a computer to execute: for extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, processing of, for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing a sum of the estimated values from said m-th mixed signal to produce an m-th separated signal; and processing of producing a signal using said first to n-th separated signals, and outputting the signal as said first signal.

Advantageous Effects of Invention

According to the present invention, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed.

BRIEF DESCRIPTION OF DRAWINGS

[FIG. 1] A block diagram showing a first embodiment of the present invention.

[FIG. 2] A block diagram showing a configuration of a filter included in FIG. 1.

[FIG. 3] A block diagram showing a configuration of a current component separating section included in FIG. 1.

[FIG. 4] A block diagram showing a second embodiment of the present invention.

[FIG. 5] A block diagram showing a configuration of an adaptive filter included in FIG. 4.

[FIG. 6] A block diagram showing a configuration of a current component separating section included in FIG. 4.

[FIG. 7] A block diagram showing a third embodiment of the present invention.

[FIG. 8] A block diagram showing a fourth embodiment of the present invention.

[FIG. 9] A block diagram showing another embodiment of the present invention.

[FIG. 10] A block diagram showing a configuration of a conventional noise canceller.

[FIG. 11] A block diagram showing a configuration of a conventional feed-back blind signal separation system for two inputs.

[FIG. 12] A block diagram showing a configuration of a feed-back blind signal separation system for three inputs.

DESCRIPTION OF EMBODIMENTS

Several embodiments of the present invention will now be described in detail with reference to the accompanying drawings by way of illustration. It should be noted that components described in the embodiments below are provided only by way of example, and it is not intended to limit the technical scope of the present invention thereto.

First Embodiment

FIG. 1 is a block diagram showing a configuration of a signal processing apparatus 100 in accordance with a first embodiment of the present invention. The description here will address a case in which signals s₁(k), s₂(k) from two sources are separated as an example. A first mixed signal x₁(k) output from a microphone 1 and a second mixed signal x₂(k) output from a microphone 2 are supplied to a past component separating section 20 at subtractors 3, 4, respectively, that serve as first, second subtracting sections. A filter 10 supplies a first estimated value (EQ. (9)) of a component based on a second output signal in the past to the subtractor 3, and a filter 12 supplies a second estimated value (EQ. (10)) of a component based on a first output signal in the past to the subtractor 4. As used herein, “current” refers to a time at k, and “past” refers to a time preceding the time k.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 9} \right\rbrack & \; \\ {{{\overset{\sim}{u}}_{1}(k)} = {\sum\limits_{j = 1}^{{N\; 1} - 1}{{w_{21}(j)}{y_{2}\left( {k - j} \right)}}}} & (9) \\ \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack & \; \\ {{{\overset{\sim}{u}}_{2}(k)} = {\sum\limits_{j = 1}^{{N\; 2} - 1}{{w_{12}(j)}{y_{1}\left( {k - j} \right)}}}} & (10) \end{matrix}$

In EQs. (9) and (10), the total sum on the right side is calculated starting with j=1, rather than j=0. That is, inputs to the filter 10 and filter 12 are y₂(k−1), y₂(k−2), . . . , y₂(k−N1+1) and y₁(k−1), y₁(k−2), . . . , y₁(k−N1+1).

The subtractor 3 subtracts an output of the filter 10 from the first mixed signal x₁(k), produces a first separated signal y′₁(k) as a result, and passes it to a current component separating section 5. The subtractor 4 subtracts an output of the filter 12 from the second mixed signal x₂(k), produces a second separated signal y′₂(k) as a result, and passes it to the current component separating section 5. The first separated signal y′₁(k) and second separated signal y′₂(k) are used to determine a first output signal and a second output signal as y₁(k), y₂(k), which are transmitted to output terminals 6 and 7, respectively. That is, the current component separating section 5 functions as an output section for outputting a signal produced using the first separated signal and second separated signal as the first signal from the signal source.

The second output signal y₂(k) is supplied to a delay element 9. Similarly, the first output signal y₁(k) is supplied to a delay element 11. The delay element 9 and delay element 11 delay the input first, second output signals by one sample, and supply them to the filter 10 and filter 12, respectively. That is, signals supplied to the filter 10 and filter 12 are the second output signal in the past and the first output signal in the past, respectively.

FIG. 2(a) is an exemplary configuration of the filter 10. The filter 10 is supplied with a second output signal in the past y₂(k−1). The second output signal in the past y₂(k−1) is transmitted to a multiplier 102 ₁ and a delay element 103 ₂ in the filter 10. The multiplier 102 ₁ multiplies y₂(k−1) by a factor of w₂₁(1) to result in w₂₁(1)·y₂(k−1), which is transmitted to an adder 101 ₂. The delay element 103 ₂ delays y₂(k−1) by one sample to result in y₂(k−2), which is transmitted to a multiplier 102 ₂ and a delay element 103 ₃. The multiplier 102 ₂ multiplies y₂(k−2) by a factor of w₂₁(2) to result in w₂₁(2)·y₂(k−2), which is transmitted to an adder 101 ₂. The adder 101 ₂ adds w₂₁(1)·y₂(k−1) and w₂₁(2)·y₂(k−2), and transmits a result to an adder 101 ₃. Thereafter, such a process is repeated by a series of delay elements and multipliers and finally an adder 101 _(N1−1) outputs a total value as an estimated value represented by EQ. (9) given above. The method comprising the series of operations is known as convolution.

On the other hand, FIG. 2(b) shows an exemplary configuration of the filter 12. The configuration and operation of the filter 12 can be represented by merely replacing the input signal y₂(k−1) with y₁(k−1), and coefficients w₂₁(j) (j=1, 2, . . . , N1−1) of the multipliers 122 ₁-122 _(N2−1) with w₁₂(j) (j=1, 2, . . . , N2−1). The other components and operations of the filter 12 are similar to those of the filter 10. Specifically, the filter 12 comprises delay elements 123 ₂-103 _(N2−1) corresponding to the delay elements 103 ₂-103 _(N1−1). The filter 12 also comprises multipliers 122 ₁-122 _(N2−1) corresponding to the multipliers 102 ₁-102 _(N1−1). It moreover comprises adders 121 ₂-101 _(N2−1) corresponding to 101 ₂-101 _(N1−1). Therefore, detailed description of each of them will be omitted here. It should be noted that the coefficients w₂₁(j) (j=1, 2, . . . , N1−1), w₁₂(j) (j=1, 2, . . . , N2−1) in the filters 10, 12 are constants, rather than functions of time k. Thus, when the transfer functions H₁₁, H₁₂, H₂₁, H₂₂ of the mixed signal generation process do not vary with time, the circuit and/or software for implementing the present embodiment can be significantly simplified.

The filter 10 and filter 12 are supplied with the second output signal in the past y₂(k−1) and the first output signal in the past y₁(k−1) delayed from the second output signal y₂(k) and first output signal y₁(k) by one sample by the delay element 9 and delay element 11, respectively. The filter 10 is therefore designed to calculate a component of the second signal s₂(k) in the past that is assumed to be mixed with the first mixed signal x₁(k), as the first estimated value (EQ. (9)). On the other hand, the filter 12 is designed to calculate a component of the first signal s₁(k) in the past that is assumed to be mixed with the second mixed signal x₂(k), as the second estimated value (EQ. (10)).

FIG. 3 is a diagram showing an internal configuration of the current component separating section 5. The output of the subtractor 3 is supplied to a multiplier 51 and a multiplier 53. The output of the subtractor 4 is supplied to a multiplier 52 and a multiplier 54. The multiplier 51 multiplies the input by a factor of v₁₁ and supplies the result to an adder 55. The multiplier 54 multiplies the input by a factor of v₂₁ and supplies the result to the adder 55. The adder 55 adds them together and outputs resulting y₁(k) as follows: [Equation 11] y ₂(k)=v ₁₂ {x ₁(k)−ũ ₁(k)}+v ₂₁ {x ₂(k)−ũ ₂(k)}  (11)

On the other hand, the multiplier 52 multiplies the input by a factor of v₂₂ and supplies the result to an adder 56. The multiplier 53 multiplies the input by a factor of v₁₂ and supplies the result to the adder 56. The adder 56 adds them together and outputs resulting y₂(k) as follows: [Equation 12] y ₂(k)=v ₁₂ {x ₁(k)−ũ ₁(k)}+v ₂₂ {x ₂(k)−ũ ₂(k)}  (12)

The results y₁(k) and y₂(k) are outputs of the current component separating section 5. EQ. (11) and EQ. (12) may be combined together as a matrix as given by EQ. (13).

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix} = {\begin{bmatrix} v_{11} & v_{21} \\ v_{12} & v_{22} \end{bmatrix}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix}}} & (13) \end{matrix}$

Consequently, the past component separating section 20 in FIG. 1 comprising the subtractors 3, 4, filters 10, 12, and delay elements 9, 11 uses output signals in the past y₁(k−j), y₂(k−j) (j>0) to separate out past components present in the mixed signals. A result thereof is supplied to the current component separating section 5, which further separates a current component.

In other words, the past component separating section 20 uses the first mixed signal x₁(k) and the second output signals in the past y₂(k−1), y₂(k−2), . . . , y₂(k−N1+1) to produce the first separated signal y′₁(k). It also uses the second mixed signal x₂(k) and the first signals in the past y₁(k−1), y₁(k−2), . . . , y₁(k−N1+1) to produce the second separated signal y′₂(k).

The current component separating section 5 is supplied with the first separated signal y′₁(k) and second separated signal y′₂(k), and produces the first output signal y₁(k) and second output signal y₂(k). That is, the first separated signal and second separated signal are used to produce a first output signal. Particularly, an estimated value of a current (time k) second signal is determined as a third estimated value using the second separated signal, removes the third estimated value from the first separated signal to produce the first output signal. The third estimated value is a component of the current (time k) second signal estimated to be mixed with the first mixed signal.

Now a confirmation will be made that in the configuration shown in. FIG. 1, the first output signal y₁(k) and second output signal y₂(k) resulting from separation from the first mixed signal x₁(k) and second mixed signal x₂(k) correspond to the first signal s₁(k) and second signal s₂(k) before mixture.

Representing the right side of EQs. (5) and (6) by a term based on the current first output signal y₁(k) and second output signal y₂(k) separated from a term based on the other factors, the following equations are obtained:

$\begin{matrix} {\mspace{20mu}\left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack} & \; \\ {{y_{1}(k)} = {{{x_{1}(k)} - {{w_{21}(0)}{y_{2}(k)}} - {\sum\limits_{j = 1}^{{N\; 1} - 1}{{w_{21}(j)}{y_{2}\left( {k - j} \right)}}}} = {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)} - {{w_{21}(0)}{y_{2}(k)}}}}} & (14) \\ {\mspace{20mu}\left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack} & \; \\ {{y_{2}(k)} = {{{x_{2}(k)} - {{w_{12}(0)}{y_{1}(k)}} - {\sum\limits_{j = 1}^{{N\; 2} - 1}{{w_{12}(j)}{y_{1}\left( {k - j} \right)}}}} = {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)} - {{w_{12}(0)}{y_{1}(k)}}}}} & (15) \end{matrix}$

Combining EQs. (14) and (15) together into a matrix format, EQ. (16) is obtained as follows:

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix} = {\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix} - \begin{bmatrix} {{w_{21}(0)}{y_{2}(k)}} \\ {{w_{12}(0)}{y_{1}(k)}} \end{bmatrix}}} & (16) \end{matrix}$

Rewriting this equation, EQ. (17) is obtained.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix} = {\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix} - {\begin{bmatrix} 0 & {w_{21}(0)} \\ {w_{12}(0)} & 0 \end{bmatrix}\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix}}}} & (17) \end{matrix}$

Reorganization of the equation in terms of y₁(k), y₂(k) gives the following equation:

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack & \; \\ {{\begin{bmatrix} 1 & {w_{21}(0)} \\ {w_{12}(0)} & 1 \end{bmatrix}\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix}} = \begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix}} & (18) \end{matrix}$

Solving the equation for y₁(k), y₂(k), the following equations are obtained:

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack & \; \\ \begin{matrix} {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix} = {\begin{bmatrix} 1 & {w_{21}(0)} \\ {w_{12}(0)} & 1 \end{bmatrix}^{- 1}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix}}} \\ {= {{\frac{1}{\Delta_{2}}\begin{bmatrix} 1 & {- {w_{21}(0)}} \\ {- {w_{12}(0)}} & 1 \end{bmatrix}}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix}}} \end{matrix} & (19) \\ \left\lbrack {{Equation}\mspace{20mu} 20} \right\rbrack & \; \\ {\Delta_{2} = {1 - {{w_{12}(0)}{w_{21}(0)}}}} & (20) \end{matrix}$

Now a new square matrix v is defined as EQ. (21), and then, EQ. (19) can be rewritten into EQ. (22) below.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack & \; \\ {v = {\begin{bmatrix} v_{11} & v_{12} \\ v_{21} & v_{22} \end{bmatrix} = \begin{bmatrix} \frac{1}{\Delta_{2}} & \frac{- {w_{21}(0)}}{\Delta_{2}} \\ \frac{- {w_{12}(0)}}{\Delta_{2}} & \frac{1}{\Delta_{2}} \end{bmatrix}}} & (21) \\ \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \end{bmatrix} = {\begin{bmatrix} v_{11} & v_{21} \\ v_{12} & v_{22} \end{bmatrix}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{1}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{2}(k)}} \end{bmatrix}}} & (22) \end{matrix}$

Since EQ. (22) is identical to EQ. (13), the first, second output signals can be obtained in the present embodiment as in EQs. (7) and (8). Specifically, under a condition that the following two equations stand, the first output signal y₁(k) corresponds to the current first signal s₁(k) generated from the first signal source and mixed with the first mixed signal. w ₂₁(j)=h ₂₁(j)/h ₂₂(j), j=0, 1, 2, . . . , N1−1 w ₁₂(j)=h ₁₂(j)/h ₁₁(j), j=0, 1, 2, . . . , N2−1

As described above, since a condition that w₂₁(0)=0 and w₁₂(0)=0 is not imposed in this embodiment, signal separation can be achieved for arbitrary coefficients w₂₁(0) and w₁₂(0) with high accuracy. That is, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed.

Second Embodiment

FIG. 4 is a block diagram showing a configuration of a signal processing apparatus 200 in accordance with a second embodiment of the present invention. The present embodiment has a similar configuration to that of the first embodiment, except that the past component separating section 20 is replaced with a past component separating section 21, the current component separating section 5 is replaced with a current component separating section 50, the filters 10, 12 are replaced with adaptive filters 40, 42, and a coefficient adaptation section 8 is added. Therefore, similar components are designated by similar reference numerals and explanation thereof will be omitted.

The coefficient adaptation section 8 produces coefficient updating information for updating coefficients used in the past component separating section 21 and current component separating section 50 in response to the output signals y₁(k), y₂(k). The produced coefficient updating information is supplied to the adaptive filters 40, 42, and current component separating section 50. The coefficient adaptation section 8 is capable of producing the coefficient updating information using a variety of coefficient adaptation algorithms. In a case that a normalized LMS algorithm is used, the coefficients w_(21,j)(k), w_(12,j)(k) are updated according to the equations below. It should be noted that while the coefficients w_(21,j), w_(12,j) have the same meaning as that of w₂₁(j), w₂₁(j) in the first embodiment, the designation as w_(21,j)(k), w_(12,j)(k) are used in the present embodiment because these coefficients are dependent upon time k.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack & \; \\ \begin{matrix} {{w_{21,j}\left( {k + 1} \right)} = {{w_{21,j}(k)} + {\mu\frac{{y_{1}(k)}{y_{2}\left( {k - j} \right)}}{\delta + {\sum\limits_{l = 0}^{{N\; 1} - 1}{y_{2}^{2}\left( {k - l} \right)}}}}}} \\ {= {{w_{21,j}(k)} + {\mu\frac{{y_{1}(k)}{y_{2}\left( {k - j} \right)}}{\sigma_{y^{2}}^{2}(k)}}}} \end{matrix} & (23) \\ \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack & \; \\ \begin{matrix} {{w_{12,j}\left( {k + 1} \right)} = {{w_{12,j}(k)} + {\mu\frac{{y_{2}(k)}{y_{1}\left( {k - j} \right)}}{\delta + {\sum\limits_{l = 0}^{{N\; 2} - 1}{y_{1}^{2}\left( {k - l} \right)}}}}}} \\ {= {{w_{12,j}(k)} + {\mu\frac{{y_{2}(k)}{y_{1}\left( {k - j} \right)}}{\sigma_{y^{1}}^{2}(k)}}}} \end{matrix} & (24) \end{matrix}$

In these equations, the constant μ represents a step size, and 0<μ<1. Moreover, δ is a small constant for avoiding division by zero. The second term on the right side of EQ. (23) designates an amount of the coefficient to be updated, which is supplied to the current component separating section 50 when j=0, and to the adaptive filter 40 when j>0. Similarly, the second term on the right side of EQ. (24) is supplied to the current component separating section 50 when j=0, and to the adaptive filter 42 when j>0. That is, the coefficients of the adaptive filters 40, 42 are updated using a correlation (correlation value) between y₁(k) and y₂(k). Thus, a gradient coefficient updating algorithm, represented by the normalized LMS algorithm, is used to update the coefficient w_(21,j)(k) of the filter 40 based on the output signal y₁(k) and modify the coefficient w_(12,j)(k) of the filter 42 based on the output signal y₂(k), whereby output signals can be obtained with high accuracy even when the transfer functions H₁₁, H₁₂, H₂₁, H₂₂ of the mixed signal generation process vary with time depending upon a change in an external environment.

FIG. 5 shows an exemplary configuration of the adaptive filter 40 and adaptive filter 42. The adaptive filter 40 and adaptive filter 42 in FIG. 5 are similar to the filters 10 and 12 in FIG. 2, except that the amount of the coefficient to be updated is supplied to multipliers 402 ₁, 402 ₂, . . . , 402 _(N1−1) and multipliers 422 ₁, 422 ₂, . . . , 422 _(N2−1). The amount of the coefficient to be updated μy₁(k)y₂(k−j)/σ²y₂ (j=1, 2, . . . , N1−1) supplied by the coefficient adaptation section 8 is supplied to the multipliers 402 ₁, 402 ₂, . . . , 402 _(N1−1) for use in coefficient updating according to EQ. (23). Similarly, the amount of the coefficient to be updated μy₂(k)y₁(k−j)/σ²y₁ (j=1, 2, . . . , N2−1) supplied by the coefficient adaptation section 8 is supplied to the multipliers 422 ₁, 422 ₂, . . . , 422 _(N2−1) for use in coefficient updating according to EQ. (24). Moreover, the amounts of coefficient updating μy₁(k)y₂(k)/σ²y₂ and μy₂(k)y₁(k)/σ²y₁ corresponding to j=0 are supplied to the current component separating section 50.

FIG. 6 is a diagram showing an exemplary configuration of the current component separating section 50. It is different from the current component separating section 5 shown in FIG. 3 in that the multipliers 501, 502, 503, 504 are supplied with coefficient updating information. The multipliers 501, 503 are supplied with μy₁(k)y₂(k)/σ²y₂, which is used to perform coefficient updating according to EQ. (23). Moreover, the multipliers 502, 503 are supplied with μy₂(k)y₁(k)/σ²y₁, which is used to perform coefficient updating according to EQ. (24).

The coefficient updating algorithm as applied herein may be one expressed by EQs. (25) and (26) below. [Equation 25] w _(21,j)(k+1)=w _(21,j)(k)+μ·ƒ{α·y ₁(k)}·g{β·y ₂(k−j)}  (25) [Equation 26] w _(12,j)(k+1)=w _(12,j)(k)+μ·ƒ{α·y ₂(k)}·g{β·y ₁(k−j)}  (26)

In these equations, f{·} and g{·} are odd functions, and α, β are constants. For f{·} and g{·}, a sigmoid function, hyperbolic tangent (tan h) or the like may be used. Since the other operations including coefficient updating are similar to those using EQs. (23) and (24), details thereof will be omitted. Thus, the correlation between the plurality of output signals y₁(k), y₂(k) can be used to modify coefficients w_(21,j)(k), w_(12,j)(k) of the filters 40, 42, whereby output signals can be obtained with high accuracy even when the transfer functions H₁₁, H₁₂, H₂₁, H₂₂ of the mixed signal generation process vary with time depending upon a change in an external environment.

According to the present embodiment as described above, coefficients used in the adaptive filters 40, 42 and current component separating section 50 may be updated depending upon an output signal, which enables signal separation to be achieved with higher accuracy corresponding to a change in an external environment.

Third Embodiment

<Configuration as an Underlying Technique>

Before explaining a third embodiment of the present invention, its underlying technique will be described with reference to FIG. 12. FIG. 12 shows the technique disclosed in NPL 2 extended to a number of microphones of three. This system comprises microphones 801-803, and output terminals 807-809. For an acoustic space from a first signal source 810 to the microphones 801-803, an impulse response h₁₁ (a transfer function H₁₁), an impulse response h₁₂ (a transfer function H₁₂), and an impulse response h₁₃ (a transfer function H₁₃) are defined. Similarly, for an acoustic space from a second signal source 820 to the microphones 801-803, an impulse response h₂₁ (a transfer function H₂₁), an impulse response h₂₂ (a transfer function H₂₂), and an impulse response h₂₃ (a transfer function H₂₃) are defined. Moreover, for an acoustic space from a third signal source 830 to the microphones 801-803, an impulse response h₃₁ (a transfer function H₃₁), an impulse response h₃₂ (a transfer function H₃₂), and an impulse response h₃₃ (a transfer function H₃₃) are defined.

On the other hand, the signal processing apparatus side comprises adaptive filters 811-816 corresponding to these impulse responses. The adaptive filter 811 supplies an output to a subtractor 804 in response to a second output y₂(k). The adaptive filter 812 supplies an output to the subtractor 804 in response to a third output y₃(k). The adaptive filter 813 supplies an output to a subtractor 805 in response to a first output y₁(k). The adaptive filter 814 supplies an output to the subtractor 805 in response to the third output y₃(k). The adaptive filter 815 supplies an output to a subtractor 806 in response to the second output y₂(k). The adaptive filter 816 supplies an output to the subtractor 806 in response to the first output y₁(k). Again, coefficients of these adaptive filters are updated as appropriate using the first to third outputs.

The microphone signals x₁(k), x₂(k), x₃(k) are expressed by the following equations when these microphones 801-803 lie sufficiently close to the first, second, third signal sources 810, 820, 830.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack & \; \\ {{x_{1}(k)} = {{s_{1}(k)} + {\sum\limits_{j = 0}^{{N\; 1} - 1}{{h_{21}(j)}{s_{2}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 3} - 1}{{h_{31}(j)}{s_{3}\left( {k - j} \right)}}}}} & (27) \\ \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack & \; \\ {{x_{2}(k)} = {{\sum\limits_{j = 0}^{{N\; 2} - 1}{{h_{12}(j)}{s_{1}\left( {k - j} \right)}}} + {s_{2}(k)} + {\sum\limits_{j = 0}^{{N\; 4} - 1}{{h_{32}(j)}{s_{3}\left( {k - j} \right)}}}}} & (28) \\ \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack & \; \\ {{x_{3}(k)} = {{\sum\limits_{j = 0}^{{N\; 5} - 1}{{h_{13}(j)}{s_{1}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 6} - 1}{{h_{23}(j)}{s_{2}\left( {k - j} \right)}}} + {s_{3}(k)}}} & (29) \end{matrix}$

Similarly to FIG. 10, the output signals y₁(k), y₂(k), y₃(k) are expressed by the following equations:

$\begin{matrix} {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 30} \right\rbrack} & \; \\ {{y_{1}(k)} = {{s_{1}(k)} + {\sum\limits_{j = 0}^{{N\; 1} - 1}{{h_{21}(j)}{s_{2}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 3} - 1}{{h_{31}(j)}{s_{3}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 1} - 1}{{w_{21,j}(k)}{y_{2}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 3} - 1}{{w_{31,j}(k)}{y_{3}\left( {k - j} \right)}}}}} & (30) \\ {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 31} \right\rbrack} & \; \\ {{y_{2}(k)} = {{s_{2}(k)} + {\sum\limits_{j = 0}^{{N\; 2} - 1}{{h_{12}(j)}{s_{1}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 4} - 1}{{h_{32}(j)}{s_{3}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 2} - 1}{w_{21,j}(k){y_{1}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 4} - 1}{{w_{32,j}(k)}{y_{3}\left( {k - j} \right)}}}}} & (31) \\ {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 32} \right\rbrack} & \; \\ {{y_{3}(k)} = {{s_{3}(k)} + {\sum\limits_{j = 0}^{{N\; 5} - 1}{{h_{13}(j)}{s_{1}\left( {k - j} \right)}}} + {\sum\limits_{j = 0}^{{N\; 6} - 1}{{h_{23}(j)}{s_{2}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 5} - 1}{w_{13,j}(k){y_{1}\left( {k - j} \right)}}} - {\sum\limits_{j = 0}^{{N\; 6} - 1}{{w_{23,j}(k)}{y_{2}\left( {k - j} \right)}}}}} & (32) \end{matrix}$

Therefore, the following conditions should be satisfied for signal separation. w _(21,j)(k)=h ₂₁(j), j=0, 1, 2, . . . , N1−1 w _(12,j)(k)=h ₁₂(j), j=0, 1, 2, . . . , N2−1 w _(31,j)(k)=h ₃₁(j), j=0, 1, 2, . . . , N3−1 w _(32,j)(k)=h ₃₂(j), j=0, 1, 2, . . . , N4−1 w _(13,j)(k)=h ₁₃(j), j=0, 1, 2, . . . , N5−1 w _(23,j)(k)=h ₂₃(j), j=0, 1, 2, . . . , N6−1

Moreover, in a general case in which the condition that the microphones 801-803 lie sufficiently close to the first, second, third signal sources 810, 820, 830 is not satisfied, signal separation is achieved provided the following equations stand. w _(21,j)(k)=h ₂₁(j)/h ₂₂(j), j=0, 1, 2, . . . , N1−1 w _(12,j)(k) =h ₁₂(j)/h ₁₁(j), j=0, 1, 2, . . . , N2−1 w _(31,j)(k)=h ₃₁(j)/h ₃₃(j), j=0, 1, 2, . . . , N3−1 w _(32,j)(k)=h ₃₂(j)/h ₃₃(j), j=0, 1, 2, . . . , N4−1 w _(13,j)(k)=h ₁₃(j)/h ₁₁(j), j=0, 1, 2, . . . , N5−1 w _(23,j)(k)=h ₂₃(j)/h ₂₂(j), j=0, 1, 2, . . . , N6−1

Configuration According to the Present Embodiment

To extract a desired signal from a mixed signal, the underlying technique described above also theoretically requires current values of other signals (signals other than the desired signal) contained in the mixed signal. On the other hand, to determine the current values of the “other signals,” a current value of the desired signal is required, thus posing a problem of reciprocity. Accordingly, coefficients (w_(12,0)(k), w_(21,0)(k), w_(31,0)(k), w_(32,0)(k), w_(13,0)(k), w_(23,0)(k) in the example above) corresponding to the current values of other output signals are set to zero in the filter to ignore them. Therefore, a desired signal may not successfully be extracted with accuracy, leading to degradation of quality of extracted output signals.

Now the third embodiment of the present invention will be described in contrast thereto with reference to a block diagram shown in FIG. 7. FIG. 7 corresponds to FIG. 1, added with a microphone to result in a total number of microphones of three. That is, it is a configuration for 3-channel signal separation. A difference from FIG. 1 is in that a filter, a delay element, a subtractor, and an output terminal are added, and the current component separating section 5 is replaced with a current component separating section 650.

The subtractor 611 is supplied with estimated values of components based on output signals in the past from filters 631, 632. The subtractor 612 is supplied with estimated values of components based on output signals in the past from filters 633, 634. The subtractor 613 is supplied with estimated values of components based on output signals in the past from filters 635, 636. These estimated values are given by EQ. (33) below.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack & \; \\ \left. \begin{matrix} {{{\overset{\sim}{u}}_{12}(k)} = {\sum\limits_{j = 1}^{{N\; 1} - 1}{{w_{12,j}(k)}{y_{1}\left( {k - j} \right)}}}} \\ {{{\overset{\sim}{u}}_{21}(k)} = {\sum\limits_{j = 1}^{{N\; 2} - 1}{{w_{21,j}(k)}{y_{2}\left( {k - j} \right)}}}} \\ {{{\overset{\sim}{u}}_{31}(k)} = {\sum\limits_{j = 1}^{{N\; 3} - 1}{{w_{31,j}(k)}{y_{3}\left( {k - j} \right)}}}} \\ {{{\overset{\sim}{u}}_{32}(k)} = {\sum\limits_{j = 1}^{{N\; 4} - 1}{{w_{32,j}(k)}{y_{3}\left( {k - j} \right)}}}} \\ {{{\overset{\sim}{u}}_{13}(k)} = {\sum\limits_{j = 1}^{{N5} - 1}{{w_{13,j}(k)}{y_{1}\left( {k - j} \right)}}}} \\ {{{\overset{\sim}{u}}_{23}(k)} = {\sum\limits_{j = 1}^{{N\; 6} - 1}{{w_{23,j}(k)}{y_{2}\left( {k - j} \right)}}}} \end{matrix} \right\} & (33) \end{matrix}$

The subtractors 611, 612, 613 subtract the estimated values as given by EQ. (33) from the first, second, third mixed signals x₁(k), x₂(k), x₃(k) supplied by the microphones 601, 602, 603, and pass results thereof to the current component separating section 650. To clarify the operation of the current component separating section 650, the operation is analyzed, as in the case of two signal separation shown in FIG. 1.

Following the case shown in FIG. 1, the equation below is obtained.

$\begin{matrix} {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack} & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix} = {\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix} - \left\lbrack \begin{matrix} {{{w_{21,0}(k)}{y_{2}(k)}} + {{w_{31,0}(k)}{y_{3}(k)}}} \\ {{{w_{12,0}(k)}{y_{1}(k)}} + {{w_{32,0}(k)}{y_{3}(k)}}} \\ {{{w_{13,0}(k)}{y_{1}(k)}} + {{w_{23,0}(k)}{y_{2}(k)}}} \end{matrix} \right\rbrack}} & (34) \end{matrix}$

Rewriting this equation, the equation below is obtained.

$\begin{matrix} {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack} & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix} = {\quad{\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix} - {\begin{bmatrix} 0 & {w_{21,0}(k)} & {w_{31,0}(k)} \\ {w_{12,0}(k)} & 0 & {w_{32,0}(k)} \\ {w_{13,0}(k)} & {w_{23,0}(k)} & 0 \end{bmatrix}{\quad\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix}}}}}} & (35) \end{matrix}$

Reorganization of the equation in terms of y₁(k), y₂(k), y₃(k) gives the following equation:

$\begin{matrix} {\mspace{79mu}\left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack} & \; \\ {{\begin{bmatrix} 1 & {w_{21,0}(k)} & {w_{31,0}(k)} \\ {w_{12,0}(k)} & 1 & {w_{32,0}(k)} \\ {w_{13,0}(k)} & {w_{23,0}(k)} & 1 \end{bmatrix}\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix}} = \begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix}} & (36) \end{matrix}$

Solving the equation for y₁(k), y₂(k), y₃(k), the following equations are obtained:

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack & \; \\ \begin{matrix} {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix} = {\begin{bmatrix} 1 & {w_{21,0}(k)} & {w_{31,0}(k)} \\ {w_{12,0}(k)} & 1 & {w_{32,0}(k)} \\ {w_{13,0}(k)} & {w_{23,0}(k)} & 1 \end{bmatrix}^{- 1}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix}}} \\ {= {\frac{1}{\Delta_{3}}\begin{bmatrix} {1 - {{w_{32,0}(k)}{w_{23,0}(k)}}} & {{{w_{31,0}(k)}{w_{23,0}(k)}} - {w_{21,0}(k)}} & {{{w_{21,0}(k)}{w_{32,0}(k)}} - {w_{31,0}(k)}} \\ {{{w_{32,0}(k)}{w_{13,0}(k)}} - {w_{12,0}(k)}} & {1 - {{w_{31,0}(k)}{w_{13,0}(k)}}} & {{{w_{31,0}(k)}{w_{12,0}(k)}} - {w_{32,0}(k)}} \\ {{{w_{12,0}(k)}{w_{23,0}(k)}} - {w_{13,0}(k)}} & {{{w_{21,0}(k)}{w_{13,0}(k)}} - {w_{23,0}(k)}} & {1 - {{w_{21,0}(k)}{w_{12,0}(k)}}} \end{bmatrix}}} \\ {\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix}} \end{matrix} & (37) \\ \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack & \; \\ {\Delta_{3} = {1 + {{w_{21,0}(k)}{w_{32,0}(k)}{w_{13,0}(k)}} + {{w_{31,0}(k)}{w_{12,0}(k)}{w_{23,0}(k)}} - {{w_{31,0}(k)}{w_{13,0}(k)}} - {{w_{32,0}(k)}{w_{23,0}(k)}} - {{w_{21,0}(k)}{w_{12,0}(k)}}}} & (38) \end{matrix}$

Now a new square matrix v₃(k) is defined as EQ. (39), and then, EQ. (40) is obtained.

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 39} \right\rbrack & \; \\ \begin{matrix} {{v_{3}(k)} = \begin{bmatrix} {v_{11}(k)} & {v_{12}(k)} & {v_{13}(k)} \\ {v_{21}(k)} & {v_{22}(k)} & {v_{23}(k)} \\ {v_{31}(k)} & {v_{32}(k)} & {v_{33}(k)} \end{bmatrix}} \\ {= \begin{bmatrix} {\left\{ {1 - {{w_{32,0}(k)}{w_{23,0}(k)}}} \right\}/\Delta_{3}} & {\left\{ {{{w_{31,0}(k)}{w_{23,0}(k)}} - {w_{21,0}(k)}} \right\}/\Delta_{3}} & {\left\{ {{{w_{21,0}(k)}{w_{32,0}(k)}} - {w_{31,0}(k)}} \right\}/\Delta_{3}} \\ {\left\{ {{{w_{32,0}(k)}{w_{13,0}(k)}} - {w_{12,0}(k)}} \right\}/\Delta_{3}} & {\left\{ {1 - {{w_{31,0}(k)}{w_{13,0}(k)}}} \right\}/\Delta_{3}} & \left\{ {{{w_{31,0}(k)}{w_{12,0}(k)}} - {{w_{32,0}(k)}/\Delta_{3}}} \right. \\ {\left\{ {{{w_{12,0}(k)}{w_{23,0}(k)}} - {w_{13,0}(k)}} \right\}\Delta_{3}} & {\left\{ {{{w_{21,0}(k)}{w_{13,0}(k)}} - {w_{23,0}(k)}} \right\}/\Delta_{3}} & {\left\{ {1 - {{w_{21,0}(k)}{w_{12,0}(k)}}} \right\}/\Delta_{3}} \end{bmatrix}} \end{matrix} & (39) \\ \left\lbrack {{Equation}\mspace{14mu} 40} \right\rbrack & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ {y_{3}(k)} \end{bmatrix} = {\begin{bmatrix} {v_{11}(k)} & {v_{12}(k)} & {v_{13}(k)} \\ {v_{21}(k)} & {v_{22}(k)} & {v_{23}(k)} \\ {v_{31}(k)} & {v_{32}(k)} & {v_{33}(k)} \end{bmatrix}\begin{bmatrix} {{x_{1}(k)} - {{\overset{\sim}{u}}_{21}(k)} - {{\overset{\sim}{u}}_{31}(k)}} \\ {{x_{2}(k)} - {{\overset{\sim}{u}}_{12}(k)} - {{\overset{\sim}{u}}_{32}(k)}} \\ {{x_{3}(k)} - {{\overset{\sim}{u}}_{13}(k)} - {{\overset{\sim}{u}}_{23}(k)}} \end{bmatrix}}} & (40) \end{matrix}$

That is, the current component separating section 650 executes linear combination calculation as given by EQ. 40 in response to the outputs of the subtractors 611, 612, 613, and transmits a result thereof to output terminals 604, 605, 606 as output signals y₁(k), y₂(k), y₃(k). The output signals y₁(k), y₂(k), y₃(k) are also transmitted to delay elements 681, 682, 683, 684, 685, 686.

The thus-determined first output signal y₁(k), second output signal y₂(k), third output signal y₃(k) are represented by EQs. (30)-(32). That is, under a condition that the following six equations stand, the first output signal y₁(k) corresponds to the current first signal s₁(k) generated from the first signal source and mixed with the first mixed signal. w _(21,j)(k)=h ₂₁(j)/h ₂₂(j), j=0, 1, 2, . . . , N−1 w _(12,j)(k)=h ₁₂(j)/h ₁₁(j), j=0, 1, 2, . . . , N2−1 w _(31,j)(k)=h ₃₁(j)/h ₃₃(j), j=0, 1, 2, . . . , N3−1 w _(32,j)(k)=h ₃₂(j)/h ₃₃(j), j=0, 1, 2, . . . , N4−1 w _(13,j)(k)=h ₁₃(j)/h ₁₁(j), j=0, 1, 2, . . . , N5−1 w _(23,j)(k)=h ₂₃(j)/h ₂₂(j), j=0, 1, 2, . . . , N6−1

In this embodiment, coefficients (w_(12,0)(k), w_(21,0)(k), w_(31,0)(k), w_(32,0)(k), w_(13,0)(k), w_(23,0)(k) in the example above) corresponding to the current values of other output signals do not need to be set to zero in the filter. Therefore, signal separation can be achieved for arbitrary coefficients with high accuracy. That is, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed.

Fourth Embodiment

FIG. 8 is a block diagram showing a fourth embodiment of the present invention. A relationship between FIGS. 7 and 8 corresponds to the relationship between FIGS. 1 and 4 except that the number of signals to be separated is modified from two to three. As a coefficient updating algorithm, a normalized LMS algorithm or an algorithm as given by EQs. (25) and (26) can be used. Therefore, further details will be omitted.

Fifth Embodiment

While the preceding description addresses a case in which a mixed signal comprised of two signals is separated in FIGS. 1 and 4, and a case in which a mixed signal comprised of three signals is separated in FIGS. 7 and 8, a more general case in which a mixed signal comprised of n signals is separated can be similarly considered. In a case that the number of microphones and the number of signal sources are both n, first to n-th output signals y₁(k), y₂(k), y₃(k), . . . , y_(n)(k) are given by the following equation:

$\begin{matrix} {\mspace{79mu}\left\lbrack {{Equation}{\mspace{11mu}\;}41} \right\rbrack} & \; \\ {\begin{bmatrix} {y_{1}(k)} \\ {y_{2}(k)} \\ \vdots \\ {y_{n}(k)} \end{bmatrix} = {\begin{bmatrix} 1 & {w_{21,0}(k)} & \ldots & {w_{{n\; 1},0}(k)} \\ {w_{12,0}(k)} & 1 & \ldots & {w_{{n\; 2},0}(k)} \\ \vdots & \vdots & 1 & \vdots \\ {w_{{1n},0}(k)} & {w_{{2n},0}(k)} & \ldots & 1 \end{bmatrix}^{- 1}\begin{bmatrix} {{x_{1}(k)} - {\sum\limits_{\underset{j \neq 1}{j = 1}}^{n}{{\overset{\sim}{u}}_{j\; 1}(k)}}} \\ {{x_{2}(k)} - {\sum\limits_{\underset{j \neq 2}{j = 1}}^{n}{{\overset{\sim}{u}}_{j\; 2}(k)}}} \\ \vdots \\ {{x_{n}(k)} - {\sum\limits_{\underset{j \neq n}{j = 1}}^{n}{{\overset{\sim}{u}}_{j\; n}(k)}}} \end{bmatrix}}} & (41) \end{matrix}$

An inverse matrix A⁻¹ of an n-th order square matrix A is given by the following equation:

$\begin{matrix} \left\lbrack {{Equation}\mspace{14mu} 42} \right\rbrack & \; \\ {A^{- 1} = {\frac{1}{\Delta_{n}}B^{T}}} & (42) \end{matrix}$

In this equation, B^(T) is a transpose of B, which is a cofactor of A. Δ_(n) is a determinant of A, |A|, and a square matrix B is given by the following equation:

$\begin{matrix} \left\lbrack {{Equation}{\mspace{11mu}\;}43} \right\rbrack & \; \\ {B = \begin{bmatrix} b_{11} & b_{21} & \ldots & b_{n\; 1} \\ b_{12} & b_{22} & \ldots & b_{n\; 2} \\ \vdots & \vdots & \ddots & \vdots \\ b_{1\; n} & b_{2\; n} & \ldots & b_{nn} \end{bmatrix}} & (43) \\ \left\lbrack {{Equation}\mspace{14mu} 44} \right\rbrack & \; \\ {b_{ij} = {\left( {- 1} \right)^{p + q}{\left. b_{pq} \right|_{{p \neq i},{q \neq j}}}}} & (44) \end{matrix}$

That is, for an arbitrary number n of signals, a column vector on the right side of EQ. (41) is determined as a first separated signal in which components generated by output signals in the past are separated. By applying thereto the inverse matrix on the right side of EQ. (41) from the left to determine a current output signal, signal separation can be achieved without explicitly using the current output signal. It should be noted that when separating a mixed signal containing n signals, it is necessary to provide n(n−1) filters for separating the past components.

Specifically, for a natural number m from one to n, estimated values of first to n-th signals in the past other than an m-th signal in the past are determined, the estimated values are removed from an m-th mixed signal to produce an m-th separated signal, and a signal produced using first to n-th separated signals is output as a first signal. Thus, first to n-th mixed signals in which n signals from the first signal to n-th signal are mixed can be used to extract the first signal. That is, by making a configuration as in the present embodiment, it is possible to separate a desired signal with high accuracy even from a mixed signal in which an arbitrary number of signals are mixed.

Another Embodiment

According to the first to fifth embodiments in the preceding description, a plurality of mixed signals are wholly processed to separate a signal. However, a process involving dividing a mixed signal into a plurality of sub-band mixed signals, processing the plurality of sub-band mixed signals to determine a plurality of sub-band output signals, and combining the plurality of sub-band output signals to determine an output signal may be contemplated. That is, any one of the embodiments described earlier may be applied after dividing a mixed signal into sub-bands to produce sub-band mixed signals, and a resulting plurality of sub-band output signals may be combined to determine an output signal. By applying sub-band processing, the number of signals can be decreased to reduce the amount of computation. Moreover, since convolution in a time domain (filtering) can be expressed by a simple multiplication, it is possible to reduce the amount of computation. Furthermore, since a sub-band signal spectrum is more planar to be closer to a white signal than a full-band signal spectrum, performance of separation is improved.

In such sub-band division processing, time-to-frequency transform such as a band division filter bank, Fourier transform, or cosine transform may be applied. In sub-band synthesis, frequency-to-time transform such as a frequency band synthesis filter bank, inverse Fourier transformation, or inverse cosine transform may be applied. Furthermore, in the time-to-frequency transform and frequency-to-time transform, a window function may be applied to reduce discontinuity at a block border. Consequently, prevention of unusual noises and calculation of accurate sub-band signals become possible.

In addition to the embodiments described above, any arbitrary combination thereof is encompassed by the scope of the present invention. Moreover, the present invention may be applied either to a system comprising a plurality of pieces of hardware or a single-unit apparatus. Furthermore, the present invention is applicable to a case in which a signal processing program in software implementing the function of any embodiment is supplied directly or remotely to a system or an apparatus. Therefore, programs installed in a computer, media for storing the programs, and WWW servers allowing download of the programs to implement the function of the present invention in the computer are encompassed by the scope of the present invention.

FIG. 9 shows a flow chart illustrating software for implementing the function of the present invention, representing that the flow chart is executed by a computer. FIG. 9 shows a configuration in which a computer 1000 applies the signal processing described regarding the first to fourth embodiments above in response to mixed signals x₁(k), x₂(k) to determine output signals y₁(k), y₂(k). Specifically, a first mixed signal and a second mixed signal in which a first signal and a second signal are mixed are first input (S1001). Next, an estimated value of the first signal in the past is determined as a first estimated value, and an estimated value of the second signal in the past is determined as a second estimated value (S1002). Next, the second estimated value is removed from the first mixed signal to produce a first separated signal (S1003). Next, the first estimated value is removed from the second mixed signal to produce a second separated signal (S1004). Furthermore, the first separated signal and second separated signal are used to produce a first output signal (S1005). The first output signal is equal to the original first signal under a certain condition. While the number of input mixed signals is two in FIG. 9, this is merely an example and the number may be an arbitrary integer n.

While the present invention has been described with reference to embodiments and examples in the preceding description, the present invention is not necessarily limited to the embodiments and examples described above, and several modifications may be made within a scope of the technical idea thereof.

The present application claims priority based on Japanese Patent Application No. 2009-229509 filed on Oct. 1, 2009, disclosure of which is incorporated herein as its entirety.

REFERENCE SIGNS LIST

1, 2, 601, 602, 603, Input terminals (microphones)

3, 4, 611, 612, 613 Subtractors

20, 21, 620 Past component separating section

5, 500 Current component separating section

6, 7, 604, 605, 606 Output terminals

8, 708 Coefficient adaptation section

9, 11, 103 ₂-103 _(N1−1), 123 ₂-123 _(N2−1), 403, 423, 681-686 Delay elements

10, 12, 631-636 Filters

51-54, 102 ₁-102 _(N1−1), 122 ₁-122 _(N2−1), 501-504 Multipliers

55, 56, 101 ₂-101 _(N1−1), 121 ₂-121 _(N2−1) Adders

40, 42, 731-736 Adaptive filters

1000 Computer 

The invention claimed is:
 1. A signal processing method of extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, comprising: determining an estimated value of said first signal in the past as a first estimated value; determining an estimated value of said second signal in the past as a second estimated value; removing said second estimated value from said first mixed signal to produce a first separated signal; removing said first estimated value from said second mixed signal to produce a second separated signal; and outputting a changing mixture, of said first separated signal and said second separated signal as said first signal, which is controlled by a mixture of said first separated signal and said second separated signal.
 2. A signal processing method according to claim 1, wherein said first estimated value is a component of the first signal in the past that is estimated to be mixed with said second mixed signal, and said second estimated value is a component of the second signal in the past that is estimated to be mixed with said first mixed signal.
 3. A signal processing method according to claim 1, comprising determining an estimated value of said second signal at the current time as a third estimated value using said second separated signal, and removing said third estimated value from said first separated signal to produce said signal.
 4. A signal processing method according to claim 3, wherein said third estimated value is a component of said second signal at the current time that is estimated to be mixed with into said first mixed signal.
 5. A signal processing method according to claim 1, wherein said first and second mixed signals are sub-band mixed signals resulting from sub-band division.
 6. A signal processing method according to claim 1, comprising: in determining said first estimated value, convoluting said first signal in the past with a first group of coefficients; in determining said second estimated value, convoluting said second signal in the past with a second group of coefficients; updating said first group of coefficients using said second signal in the past; and updating said second group of coefficients using said first signal in the past.
 7. A signal processing method according to claim 1, comprising: in determining said first estimated value, convoluting said first signal in the past with a first group of coefficients; in determining said second estimated value, convoluting said second signal in the past with a second group of coefficients; updating said first and second groups of coefficients using a value of correlation between said first signal in the past and said second signal in the past.
 8. A signal processing method of extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, comprising: for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing the estimated values from an m-th mixed signal to produce an m-th separated signal; and producing a changing mixture of said first to n-th separated signals, and outputting the signal as said first signal, wherein the changing mixture is controlled by a mixture of said first n-th separated signals.
 9. A signal processing method according to claim 8, wherein said estimated values are components of the first to n-th signals in the past other than the m-th signal in the past that are estimated to be mixed with said m-th mixed signal.
 10. A signal processing method according to claim 8, comprising determining estimated values of said second to n-th signals at the current time using said first to n-th separated signals, and removing the estimated values of said second to n-th signals at the current time from said first separated signal to produce said first signal.
 11. A signal processing method according to claim 8, wherein the estimated values of said second to n-th signals at the current time are components of said second to n-th signals at the current time that are estimated to be mixed with said first mixed signal.
 12. A signal processing method according to claim 8, wherein said first to n-th mixed signals are sub-band mixed signals resulting from sub-band division.
 13. A signal processing method according to claim 8, comprising: in determining said estimated values, convoluting said first to n-th signals in the past other than the m-th signal in the past with a plurality of coefficients; and updating said plurality of coefficients using said first signal in the past.
 14. A signal processing method according to claim 8, comprising: in determining said estimated values, convoluting said first to n-th signals in the past other than the m-th signal in the past with a plurality of coefficients; and updating said plurality of coefficients using a value of correlation among said first to n-th signals in the past.
 15. A signal processing apparatus comprising: a first filter configured to produce, from a first mixed signal generated to have a first signal and a second signal mixed, an estimated value of said second signal in the past as a second estimated value; a first subtracting section configured to remove said second estimated value from said first mixed signal to produce a first separated signal; a second filter configured to produce, from a second mixed signal generated to have the first signal and second signal mixed, an estimated value of said first signal in the past as a first estimated value; a second subtracting section configured to remove said first estimated value from said second mixed signal to produce a second separated signal; and an output section configured to output a changing mixture, of said first separated signal and said second separated signal as said first signal, which is controlled by a mixture of said first separated signal and said second separated signal.
 16. A signal processing apparatus comprising: a filter, for each natural number m from 1 to n, producing, from first to n-th mixed signals generated to have n signals from a first signal to an n-th signal mixed, estimated values of the first to n-th signals in the past other than an m-th signal in the past; a subtracting section for removing said estimated values from said first to n-th mixed signals to produce first to n-th separated signals; and an output section configured to output a changing mixture, of said first to n-th separated signals as said first signal, which is controlled by a mixture of said first to n-th separated signals.
 17. A non-transitory, computer readable medium comprising a signal processing program causing a computer to execute: for extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, processing of determining an estimated value of said first signal in the past as a first estimated value; processing of determining an estimated value of said second signal in the past as a second estimated value; processing of removing said second estimated value from said first mixed signal to produce a first separated signal; processing of removing said first estimated value from said second mixed signal to produce a second separated signal; and processing of outputting a changing mixture, of said first separated signal and said second separated signal as said first signal, which is controlled by a mixture of said first separated signal and said second separated signal.
 18. A non-transitory, computer readable medium comprising a signal processing program causing a computer to execute: for extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, processing of, for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing a sum of the estimated values from said m-th mixed signal to produce an m-th separated signal; and processing of producing a changing mixture, of said first to n-th separated signals, and outputting the signal as said first signal, wherein the changing mixture is controlled by a mixture of said first to n-th separated signals. 